The main objective of the present work is to correlate quarter-point angle and nuclear radius or nuclear matter distribution. Various phenomenological formulae with parameters for strong absorption radius Rs are obtained and compared by fitting the experimental data of quarter point angle extracted from nuclear elastic scattering reaction systems. The parameterized formula of Rs related to the isospin and binding energy is recommended, that gives a good reproduction of nuclear matter radii of halo nuclei.
Mass number dependence of the nuclear radii is closely related to the nuclear matter properties. It is known that the most of nuclei exhibit some deformation. We discuss how the nuclear density profile is modified by the nuclear deformation to elucidate the enhancement mechanism of the nuclear radii through a systematic investigation of neutron-rich Ne, Mg, Si, S, Ar, Ti, Cr, and Fe isotopes. Skyrme-Hartree-Fock calculations are performed in a three-dimensional Cartesian grid to describe the nuclear deformation in a non-empirical way. The role of the nuclear deformation on the nuclear density …
Meaningful predictions for electric quadrupole (E2) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown E2 observables. However, converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) approaches. Matrix elements of the E2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergenc…
To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl et al. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 $σ$ to 2 $σ$. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon-nucleon interactions derived from chiral effective…
Measurements of atomic transitions in different isotopes offer key information on the nuclear charge radius. The anticipated high-precision experimental techniques, augmented by atomic calculations, will soon enable extraction of the higher-order radial moments of the charge density distribution. To assess the value of such measurements for nuclear structure research, we study the information content of the fourth radial moment $\rf$ by means of nuclear density functional theory and a multiple correlation analysis. We show that $\rf$ can be directly related to the surface thickness of nuclear …
QCD and nuclear physics. How to explain the coincidence between the action radius of nuclear forces and the characteristic scale of the neutron-neutron electrostatic interaction?
The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, tr…
We find a new method to deduce nuclear radii from proton-nucleus elastic scattering data. In this method a nucleus is viewed as a ``black'' sphere. A diffraction pattern of protons by this sphere is equivalent to that of the Fraunhofer diffraction by a circular hole of the same radius embedded in a screen. We determine the black sphere radius in such a way as to reproduce the empirical value of the angle of the observed first diffraction peak. It is useful to identify this radius multiplied by $\sqrt{3/5}$ with the root-mean-square matter radius of the target nucleus. For most of stable isotop…
We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determine…
Nuclear structure corrections to the Lamb shift in $μ^3$He$^+$ and $μ^3$H
测量类氢μ子原子中的2S-2 P兰姆位移允许以高精度提取其核电荷半径，该精度受到原子核结构校正中的不确定性的限制。由此提取的质子的电荷半径被发现与CODATA值相差7 σ，这已经成为尚未解决的“质子半径之谜”。目前，进一步的实验瞄准了氢和氦的同位素：精确提取它们的半径可能会为解决这个难题提供线索。我们提出了第一个从头计算的原子核结构修正，包括核极化修正，在$μ^3$ He $^+$和$μ^3$ H的2S-2 P跃迁，并评估固体理论误差棒。我们的预测将原子核结构修正的不确定性降低到几个不确定性的水平，并将有助于正在进行的$μ^3$ He $^+$实验。我们也支持镜像$μ\,^3$ H系统作为进一步探测核子极化率的候选者，并为这个难题提供更多的光。
The kernel ridge regression (KRR) method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$ formulae, and their improved versions by considering the isospin dependence are adopted as examples. The parameters in these six formulae are refitted using the Levenberg-Marquardt method, which give better results than the previous ones. The radius for each nucleus is predicted with the KRR network, which is trained with the deviations between experimental and calculated nuclear ch…
By directly inverting several neutron star observables in the three-dimensional parameter space for the Equation of State of super-dense neutron-rich nuclear matter, we show that the lower radius limit for PSR J0740+6620 of mass $2.08\pm 0.07~M_{\odot}$ from Neutron Star Interior Composition Explorer (NICER)'s very recent observation sets a much tighter lower boundary than previously known for nuclear symmetry energy in the density range of $(1.0\sim 3.0)$ times the saturation density $ρ_0$ of nuclear matter. The super-soft symmetry energy leading to the formation of proton polarons in this de…
Robust ab initio predictions for dimensionless ratios of E2 and radius observables. II. Estimation of E2 transition strengths by calibration to the charge radius
Up to now, all charge radius measurements of the proton and deuteron assumed uniform spheroidal charge distribution. We investigate the nuclear deformation effects on these charge radius measurements by assuming a uniform prolate charge distribution for the proton and deuteron. We solve the energy levels of the corresponding muonic and electric atoms with such deformed nucleus and present how the purely quadruple deformation of proton and deuteron affects their Lamb shifts. The numerical results suggest that the deformation of proton and deuteron leads to that the charge radius extracted from …
The determination of the equation of state (EOS) for nuclear matter has been one of the biggest problems in nuclear astrophysics, because the EOS is essential for determining the properties of neutron stars. To constrain the density-dependence of the nuclear symmetry energy, several nuclear experiments, e.g., reported by the S$π$RIT and PREX-II collaborations, have recently been performed. However, since their uncertainties are still large, additional constraints such as astronomical observations must be crucial. In addition, it is interesting to see the effect of their reported value on neutr…
We put forward a method for determination of the kaon radius from the spectra of kaonic atoms. We analyze the few lowest transitions and their sensitivity to the size of the kaon for ions in the nuclear charge range Z = 1 - 100, taking into account finite-nuclear-size, finite-kaon-size, recoil and leading-order quantum-electrodynamic effects. Additionally, the opportunities of extracting the kaon mass and nuclear radii are demonstrated by examining the sensitivity of the transition energies in kaonic atoms.
We studied the charge radius ($r_{c}$), neutron radius ($r_n$), and neutron skin-thickness ($Δr=r_n-r_p$) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) with effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement are noted. We additionally assessed the two-neutron separation energy ($S_{2n}$) to mark the drip line nuclei of the considered isotopic s…
In view of the future plans to measure the Lamb shift in muonic Lithium atoms we address the microscopic theory of the $μ$-$^6$Li$^{2+}$ and $μ$-$^7$Li$^{2+}$ systems. The goal of the CREMA collaboration is to measure the Lamb shift to extract the charge radius with high precision and compare it to electron scattering data or atomic spectroscopy to see if interesting puzzles, such as the proton and deuteron radius puzzles, arise. For this experiment to be successful, theoretical information on the nuclear structure corrections to the Lamb shift is needed. For $μ$-$^6$Li$^{2+}$ and $μ$-$^7$Li$^…
Motivated by the unknown nature of the $2.50-2.67\,M_\odot$ compact object in the binary merger event GW190814, we study the maximum neutron star mass based on constraints from low-energy nuclear physics, neutron star tidal deformabilities from GW170817, and simultaneous mass-radius measurements of PSR J0030+045 from NICER. Our prior distribution is based on a combination of nuclear modeling valid in the vicinity of normal nuclear densities together with the assumption of a maximally stiff equation of state at high densities, a choice that enables us to probe the connection between observed he…
A phenomenological alpha-cluster model based on np-pair interactions and the charge symmetry of nuclear force allows one to estimate the Coulomb energy, the Coulomb radius R_C, the Coulomb energy of the last proton interaction with the residual nucleus and the radius of its position R_p in a symmetrical nucleus. The values R_C and R_p obtained for the symmetrical nuclei with 5<= Z<=45 are used in a long standing task of determination of the parameters of the Woods-Saxon potential of neuton/proton bound state used in DWBA analysis of direct one nucleon transfer reactions. According to the charg…
The discovery of the proton-radius puzzle and the subsequent deuteron-radius puzzle is fueling an on-going debate on possible explanations for the difference in the observed radii obtained from muonic atoms and from electron-nucleus systems. Atomic nuclei have a complex internal structure that must be taken into account when analyzing experimental spectroscopic results. Ab initio nuclear structure theory provided the so far most precise estimates of important corrections to the Lamb shift in muonic atoms and is well poised to also investigate nuclear structure corrections to the hyperfine spli…
We study the effects of free space nucleon radius on nuclear matter and neutron stars within the framework of quark mean field model. The nucleon radius is treated self-consistently with this model, where quark confinement is adjusted to fit different values of nucleon radius. Corrections due to center-of-mass motion, quark-pion coupling, and one gluon exchange are included to obtain the nucleon mass in vacuum. The meson coupling constants that describe the behavior of many-body nucleonic system are newly-constructed by reproducing the empirical saturation properties of nuclear matter, includi…
We explore the connection between the stiffness of an hadronic equation of state (EoS) with a sharp phase transition to quark matter to its tidal deformability. For this we employ a hadronic relativistic mean field model with a parameterized effective nucleon mass to vary the stiffness in conjunction with a constant speed of sound EoS for quark matter. We compute multiple scenarios with phase transitions according to the four possible cases of a hybrid star EoS with a stable second branch. We demonstrate at the example of GW170817 how the effective nucleon mass can be constrained by using grav…
